Ontology

Collection of concepts and their relationships, in a machine-readable format. An ontology may contain facts about the world, like Donald Trump is the 45th president of USA, but more importantly, pre-factual knowledge, like presidents are human and in order to be a president at a given time, one must be alive at the time.

This zettel is really long, because I’m reading way too many papers about ontologies. Here’s TL;DR.

Ontology has:

  • Taxonomy as a backbone (cat is an animal, animal is a living-entity, …)

It may also have some of the following

  • Other, non-hierarchical relations (cats are cute)
  • Rules/axioms to derive facts that are not explicitly encoded by the ontology (motherhood is a special case of parenthood; Mary is John’s mother -> Mary is John’s parent)

Origins and etymology

Quotes from “Approaches to Legal Ontologies: Theories, Domains, Methodologies: 1 (Law, Governance and Technology Series)”

The name “ontology” has its roots in philosophy.

ontology is understood as “the science of what is, of the kinds and structures of objects, properties, events, processes and relations in every area of reality” (Smith 2003)

If representing the true nature of reality sounds too ambitious, we can also say that ontologies “are meant to provide the structures though which agents conceptualise (possibly wrongly) reality, rather than reality itself.”

Taxonomy

The basic building block of an ontology is a hierarchy of concepts (or “terms”). Higher nodes represent general concepts, lower nodes more specific. For example, see the trees below.

         Furniture
          /    \
       Chair   Table
       /  \    /  \
Armchair … … … … KitchenTable

Depending on the ontology, the concepts may be classes, individuals (or “particulars”), properties or any other term that an ontology engineer likes. Quote from Mascardi et al. (2007) A Comparison of Upper Ontologies, comparing SUMO#and DOLCE:

DOLCE has been carefully crafted with respect to strong principles. DOLCE is an “ontology of particulars”; it does have universals (classes and properties), but the claim is that they are only employed in the service of describing particulars. In contrast, SUMO could be described as an ontology of both particulars and universals. It has a hierarchy of properties as well as classes. This is a very important feature for practical knowledge engineering, as it allows common features like transitivity to be applied to a set of properties, with an axiom that is written once and inherited by those properties, rather than having to be rewritten, specific to each property.

Here is an example (still made up) of classes and individuals. AirportsInSweden is a subclass of AirportsInEurope, and Arlanda is an instance of AirportsInSweden. If the ontology contains an appropriate axiom (more on those later) about class inheritance, then a reasoner will know that Arlanda is also an instance of AirportsInEurope.

          AirportsInEurope                        -- classes
           /      |      \
AirportsInSweden … … … AirportsInGreatBritain     -- classes
        /    /    |      /     \
    Arlanda  …    …   Heathrow  …                 -- individuals

Whether an ontology has “classes” and “individuals” or some other concepts, is a matter of the particular ontology.

or combining ontologies on different domains and levels of detail, see Interoperability between ontologies#.

Relationships

So far we’ve seen only taxonomy membership in a strict tree structure.

  • Spice Girls is-a Band
  • Wannabe is-a Song

But we can also have other relationships.

  • Spice Girls perform Wannabe
  • Wannabe year 1996

Furthermore, the relation links themselves can be the subject or object in another relation.

  • Perform is-a Action
  • is-a is-a Relation

See RDF, a data model based on subject–predicate–object triples.

Axioms / Assertions / Theories / Facts / Rules

Depending on the language of the ontology, it may be possible to express more complex relationships between the concepts. Depending on the ontology, these may be called with a variety of names. For instance, SUMO# uses the term axiom; Cyc# uses assertions.

In this zettelkasten, I will use the term axiom, unless I’m talking about a specific ontology that has established jargon.

Some examples of axioms:

  • all mothers are parents (source)
  • if a person is sleeping, they can’t perform an intentional action (source)

Reasoning

Based on the terms and the axioms, we can now ask questions and draw conclusions that aren’t explicitly stated before.

Pease gives the following example in Why use OWL:

[T]he statements

(motherOf subProperty parentOf)
(Mary motherOf Bill)

when stated in OWL, allows you to conclude

(Mary parentOf Bill)

based on the logical definition of “subProperty” as given in the OWL spec.

Mapping to lexical resources

Niles and Pease (2003) map mid-level entries from SUMO# to WordNet#. WordNet itself has some relations like synonymy and hypernymy, and I’m not quite sure how they work together with the relations of an ontology (TODO: read the linked paper).

Main point is that a concept in an ontology corresponds to one or more synonym sets in WordNet. Consider a corner of ontology like the following:

            Entity
            /    \
      Abstract   Physical
      / | | \    /    |  \
  Attribute …  …     …    …
    / | \
       Measure
       /     \
TimeMeasure  LengthMeasure

The concept Measure is mapped to a number of WordNet synonym sets, such as

  • space 00014887 ‘3-dimensional expanse in which everything is located’
  • time 15160774 ‘the fourth coordinate that is required (along with three spatial dimensions) to specify a physical event’
  • length 05136466 ‘the linear extent in space from one end to the other’
  • …

And LengthMeasure is mapped only to 00014887 space and 05136466 length.

Use of “Ontology” in Expert Systems

The word ontology with regard to expert systems is also used to refer to the data structure of known data objects, and their relationships to one another. This may not be an external resource such as a pre-populated OWL ontology, but may be defined inside the programming language itself, for example as object-oriented programming class definitions.

In this context the “ontology” is usually distinguished from the “rules”.

As an example, in Oracle Intelligent Advisor, the “Data” tab sets out objects, sub-objects, attributes, and relationships, including cardinality and bi-directionality. These are all things that ontology languages like OWL allow you to specify, and which could conceivebaly be imported from an OWL library.

“Rules” on the other hand, specify the implications arising from different conditions, and have a semantic meaning which is more complicated than can be expressed in the logic of ontology languages, which are usually based on Description Logic.

In this sense “a person must pay taxes on their income” is a rule, but the fact that “a person has an income” is an ontological fact, which might be expressed as a class definition, and referred to as person.income.

Languages for writing ontologies

language/ontology
Gellish#
OWL#

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